Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

The temperature has a great contribution to the mesh stiffness and backlash of the gear pair. Presence of thermal deformation caused by temperature will complicate the gear teeth interaction. In this paper, the thermal time-varying stiffness model and thermal time-varying backlash model are proposed with the consideration of tooth profile error and total thermo-elastic deformation consists of the teeth deformation, teeth contact deformation, and gear body-induced deformation. The key parameters of thermo-elastic coupling deformation affected by temperature are calculated. Based on the proposed models, the influencing mechanism of temperature on the tooth profile error, mesh stiffness, total deformation, and backlash are revealed. The effects of shaft radius and torque load on the thermal stiffness and thermal backlash are studied. The proposed thermal stiffness and backlash calculation model are proven to be more comprehensive and the correctness is validated.

Characterization and Modeling of LV Cables Considering External Parameters for Distribution Networks

In response to the climate emergency, new uses are plugged to low voltage (LV) electrical networks. The development of self-consumption complicate the LV grid operation, and force distribution system operators (DSOs) to better model and characterize their networks. DSOs mainly use a three-conductor model (3 CM) to compute power flows, and consider error margins of 2% for voltage profiles to reflect their model inaccuracy. The characteristics of the future LV grids call into question these margins, and the models used. In this paper, a four-conductor model (4 CM), and an additional model named 4 CMext, that considers external parameters (i.e., cable temperature, ground electrical resistivity, and value/number of the earthing resistances) are proposed. The best model for cable characterization and voltage profile calculation is chosen; the 4 CMext is more adapted for the characterization, and corresponds with the finite element model, with an error margin of 4%, experimental measurements of 15%, and French cable manufacturer data of 0.5%. For the voltage profile, the 4 CMext provides a more detailed view of the critical cases that could lead to a violation of the limits of the EN 50160 standard than 3 CM and 4 CM. Violations of high or low voltages are underestimated by two to six times by the 3 CM and 4 CM. Not considering external parameters can lead to a voltage profile error of above 3%. In this paper, we recommend that DSOs use the 4 CMext to represent LV networks, which would allow LV networks to be used closer to their physical limits, and avoid or postpone network reinforcements.

A normal section plane method for profile error analysis of five-axis machine tools based on the ideal tool flank milling surface

The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.

Research on the profile modification of power skiving tool for internal gears

Power skiving provides an effective solution and considerable machining efficiency for the machining of internal gears. The tool profile design and the reusability after resharpening is critical in gear machining. In this paper, a tool profile correction method based on the error inverse complement of involute profile is proposed. The mathematical model of involute cutter with rake angle and relief angle is established, and the profile error relative to the target gear is calculated by using the tool of this mathematical model. The distribution of gear profile error is fitted by fifth-order multinomial, and the multinomial function of fitting was attached to the cutter profile. The theoretical error of the target gear profile is in 10e-7mm order of magnitude through the calculation of fewer iterations. The distribution of the coefficient of the error multinomial along the resharpening direction is obtained by linear programming. The result shows that the tool designed by this method has almost negligible error accuracy and good repeatability.

Investigation on Morphology and Mechanical Properties of Rod Units in Lattice Structures Fabricated by Selective Laser Melting

Selective laser melting (SLM) fabrication of lattice structures has attracted considerable interest due to its many immanent advantages, such as high specific strength. A wide variety of lattice structures have been designed and fabricated. However, as a vital prerequisite for design optimization, a clear relation between the process constraint of SLM and the apparent properties of the fabricated lattice structure has received much less attention. Therefore, this work systematically investigates the characterization and preformation of rod units, which are the basic components of lattice structures, so as to evaluate the SLM manufacturability of lattice structures. A series of rod units with different inclination angles and diameters were fabricated by SLM. Their morphology and mechanical properties were measured by scanning electron microscope observation and a tensile test, respectively. The inclination angle was found to have significant effects on profile error and little effect on mechanical properties. The higher the inclination angle, the larger the profile error. The characteristic diameter had no significant correlation with profile errors and mechanical properties. Based on systematic studies, a formula is proposed to evaluate the cross-sectional area of the fabricated rod units and further estimate their load capacity. This has important implications for optimizing the design of lattice structures fabricated by SLM.

Implementation of Artificial Intelligence in Bending Analysis of Propeller/Fan Blade

The bending of the blade is one of the dominating factors in the manufacturing considerations as it directly impacts the performance of propeller in terms of propulsion efficiency. The blade moulding equipment developed in-house has extensive control over the bending. After understanding the working mechanism of the instrument, a simplified model is created to perform the numerical analysis over the blade to inspect the nature of deformation. The theoretical and numerical analysis is performed assuming the contact between the rods of the equipment, and the blade is frictionless. The region of the bent propeller blade is scanned to know the deviation error. The AI tool to predict the required force per region for the blade the reformation was employed. Also, numerous factors contribute to the effect of net spring back occurs in the metal sheet. However, because of the limitations on the availability of the literature regarding formulation to add strain hardening and sheet preheating effects, one needs to approximate the solution. To approximately predict spring-back, factors such as bending force, material properties, sheet thickness, and boundary (support) conditions considered in the theoretical analysis and testing. The performance measurement was carried out for the same blade after the reformation and was found equally efficient (maximum error up to 7%). The error is caused due to the dent marks over the region and restored profile error.

Modelling and experiment of gear hob tooth profile error for relief grinding

Gear hob is an important tool that is most used in gear processing. Hob accuracy directly exerts an overwhelming influence on the quality of the processed gear. Generally, the hob tooth profile accuracy is mainly determined by relief grinding process. Studies on tooth profile errors of gear hobs caused by severe friction and cutting with the high-speed rotation of the wheel during the form grinding machining of hobs are limited. Thus, a theoretical model of the tooth profile error prediction under different machining parameters was established based on the analysis of coupling influence of high temperature and high strain rate on gear hobs in the relief grinding process. The model was completed on the basis of the dynamic explicit integral finite element method of thermo-mechanical coupling. Through the prediction model, the influence of the grinding depth ap, feed speed Vw and grinding speed Vs on the tooth profile error can be analysed. In addition, an algorithm for accurately calculate the grinding wheel axial profile by combining instantaneous envelope theory and hob normal tooth profile was proposed. The hob relief grinding experiments were carried out using the proposed grinding wheel profile algorithm. The relative error of the prediction obtained by comparing the calculation results of the prediction model with the experimental results is within 10%. Results prove the validity of the prediction model. This finding is greatly important for optimising the accuracy of hob relief grinding.

The calculation of the allowable diametrical inaccuracy of the cycloidal driving bores in a cycloidal drive with a given profile error and transmission ratio fluctuation

Cycloidal drives are getting more and more widespread due to their beneficial properties. The greatest advantage of these transmissions compared to other general-purpose industrial transmissions, but even compared to the more widespread types of planetary gears, is their ability to operate with large transmission ratios and good efficiency under larger performance density. A smaller amount of play and the minimal fluctuation of transmission ratios, which fundamentally define the kinematic properties of these high precision premium transmissions, can only be achieved by increasing the manufacturing accuracy, decreasing the magnitude of manufacturing errors and limiting the tolerance field. The current research, has focused on finding the allowable manufacturing accuracy of transmissions that are primarily manufactured by small scale or by one-off production, and discusses the effect of the cycloidal driving bores diametrical inaccuracy in a cycloidal disc, that was manufactured with wire electrical discharge machining and contains profile defects.